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The original version of This story It appeared in How much magazine.
Pose a question to a Magic 8 ball, and he will answer yes, no, or something annoying undecided. We think about it as a children’s toy, but theoretical computer scientists use a similar tool. They often imagine that they can consult hypothetical devices called oracles that can answer instantaneously and correct specific questions. These fantasy thinking experiments have inspired new algorithms and have helped researchers map the calculation panorama.
Researchers invoking oracles work in a computer sub -computing called theory of computational complexity. They are concerned about the inherent difficulty of problems, such as determining whether a number is cousin or the search for the shortest route between two points in a network. Some problems are easy to solve, others seem much more difficult but have easy to verify solutions, while others are easy for Quantum computers But apparently hard for the commons.
Complexity theorists want to understand if these apparent differences in difficulty are fundamental. Is there anything intrinsically difficult in certain problems, or are we simply not intelligent enough to find a good solution? Researchers address such questions classifying problems in “complexity classes“-All easy problems go in a class, for example, and all easy control problems go in another, and demonstrating theorems about relationships between those classes.
Unfortunately, the mapping of the landscape of computational difficulty has turned out to be, well, difficult. Then, in the mid -1970s, some researchers began studying what would happen if the calculation rules were different. That’s where the oracles enter.
Like Magic 8 Balls, oracles are devices that immediately answer questions of themselves or not without revealing anything about its internal functioning. Unlike Magic 8 balls, they always say yes or no, and they are always correct, an advantage of being fictional. In addition, any oracle given only a specific type of question will answer, such as “Is this number prime?”
What makes these fictitious devices useful to understand the real world? In short, they can reveal hidden connections between different kinds of complexity.
Take the two most famous kinds of complexity. There is a class of problems that are easy to solve, which researchers call “P”, and the class of problems that are easy to verify, which researchers call “NP”. Are all easy to control problems easy to solve? If so, that would mean that NP would be equal to P, and all encryption would be Easy to break (among other consequences). Complexity theorists suspect that NP is not equal to P, but they cannot prove it, although they have been trying to specify the relationship between the two classes for Over 50 years.
Oracles have helped them better understand what they are working with. Researchers have invented oracles that answer questions that help solve many different problems. In a world where each computer had a direct line for one of these oracles, all the easy -to -control problems would also be easy to solve, and P would be equal to NP. But other less useful oracles have the opposite effect. In a world populated by these oracles, P and NP would be demonstrably different.
